I don't think this is something that is really quantifiable. Furthermore, it seems to me that different basses' tones are not necessarily made up of the same elements, or not to the same degree. For instance, my old jazz bass's sound would vary quite a bit depending on whether I used nickel strings or stainless steel strings. In contrast, stingrays all sound quite similar regardless of the strings used on them. Not to say that the type of strings makes no difference, but it is much easier to tell rounds from flats on a jazz than it is on stingray to my ears. I would assume that other factors have varying effects on the tones of varying basses.

The amp totally makes my sound happen. Usually when I'm going DI my bass sounds pretty crummy, but as soon as I plug it into my amp, I get a great growl, and great Marcus Miller slap tone. My amp is great.